Guaranteed‐cost consensus for multiagent networks with Lipschitz nonlinear dynamics and switching topologies

• Published in: International journal of robust and nonlinear control Vol. 28; no. 7; pp. 2841 - 2852
• Main Authors: Xi, Jianxiang, Fan, Zhiliang, Liu, Hao, Zheng, Tang
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.05.2018
• Subjects: Computer simulation; guaranteed‐cost consensus; Linear matrix inequalities; Lipschitz condition; Lipschitz nonlinearity; Mathematical analysis; Matrix methods; multiagent network; Multiagent systems; Nonlinear dynamics; Riccati equation; Switching theory; switching topology; Topology
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4051

Summary Guaranteed‐cost consensus for high‐order nonlinear multiagent networks with switching topologies is investigated. By constructing a time‐varying nonsingular matrix with a specific structure, the whole dynamics of multiagent networks is decomposed into the consensus and disagreement parts with nonlinear terms, which is the key challenge to be dealt with. An explicit expression of the consensus dynamics, which contains the nonlinear term, is given and its initial state is determined. Furthermore, by the structure property of the time‐varying nonsingular transformation matrix and the Lipschitz condition, the impacts of the nonlinear term on the disagreement dynamics are linearized, and the gain matrix of the consensus protocol is determined on the basis of the Riccati equation. Moreover, an approach to minimize the guaranteed cost is given in terms of linear matrix inequalities. Finally, the numerical simulation is shown to demonstrate the effectiveness of theoretical results.